Modelling concentric contraction of muscle using an improved cross-bridge model

Despite its overwhelming acceptance in muscle research, the cross-bridge theory does not account for all phenomena observed during muscular contractions. A phenomenon which has received much attention in the biomechanics literature, but has evaded convincing explanation and is not accounted for in the formulation of the classic cross-bridge theory, is the persistent aftereffects of muscular length changes on force production. For example, following muscle shortening, the isometric force of a muscle is depressed for a long time period (>5 s) compared to the corresponding isometric force following no length change. In the present study, the classic cross-bridge model was modified in two ways in an attempt to account for the force depressions following muscle shortening. First, the steady-state force depressions following shortening were described by a single scalar variable: the work performed by the muscle during shortening; and second, the dynamic, history-dependent cross-bridge properties were described using a fading memory function. The proposed model was developed and tested for shortening of the cat soleus at constant speeds ranging from 4 to 32 mm/s, for shortening at changing speeds, and for shortening of different magnitudes ranging from 2 to 10 mm. The history-dependent forces during shortening and the steady-state force depressions following shortening were well captured with the modified cross-bridge model. The present model contains two mathematically simple adaptations to the classic cross-bridge model, and is the first such model to account for the long-lasting force depressions following muscle shortening using a single scalar variable.